# [R] permutation test assumption?

Greg Snow Greg.Snow at imail.org
Wed Apr 9 21:11:26 CEST 2008

```A few comments,

My first impression on reading that abstract was that it was complete nonsense.  After thinking a bit about it and skimming the full article I decided that it was nonsense, but nonsense that is important to research and discuss (and therefore the paper is useful).

Why is it nonsense?  The permutation test is a test of the null hypothesis that the 2 (or k) groups are from the same distribution (or identically distributed, or exchangable).  The abstract says that they looked at the type I error rate when the 2 groups had different variances or other differences.  The type I error is defined when the null hypothesis is true, so computing a type I error rate when the null is by definition false does not make sense.

However, statisticians often do analyses where all the assumptions are not necessarily true (is any population really distributed as a normal), but the tests are close enough.  So with modern tools it is not suprising to see people doing permutation tests without understanding what they are really testing and the results may be close enough (or they might not be).  The contribution of this paper is to test and see if the results are close enough or not when you use a permutation test to test the null that the means are equal when there are other differences in the groups.  Their answer is that no, the results are not close enough and they suggest that if you want to test for equality of means, but not identical distributions, then don't use a permutation test.

To expand on Thierry's original answer:

If you are testing the correct hypotheses and doing a permutation test correctly, then
"You can do permutation tests on an unbalanced design" and it will still be a correct test.  Unbalance could affect the power, which you would want to take into account when designing a study, but does not affect the correctness of the test (when used properly).

Hope this helps,

--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
(801) 408-8111

> -----Original Message-----
> From: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org] On Behalf Of João Fadista
> Sent: Tuesday, April 08, 2008 4:10 PM
> To: ONKELINX, Thierry; r-help at r-project.org
> Subject: Re: [R] permutation test assumption?
>
> Dear Thierry,
>
> Thanks for the reply. But as you may read in the paper
> http://bioinformatics.oxfordjournals.org/cgi/content/abstract/
> 22/18/2244 when the sample sizes are not the same there may
> be an increase in the Type I error rate.
>
>
> Best regards,
>
>
> ________________________________
>
> De: ONKELINX, Thierry [mailto:Thierry.ONKELINX at inbo.be]
> Para: João Fadista; r-help at r-project.org
> Assunto: RE: [R] permutation test assumption?
>
>
>
> Dear João,
>
> You can do permutation tests on an unbalanced design.
>
> HTH,
>
> Thierry
>
>
> --------------------------------------------------------------
> --------------
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute
> for Nature and Forest Cel biometrie, methodologie en
> kwaliteitszorg / Section biometrics, methodology and quality
> assurance Gaverstraat 4 9500 Geraardsbergen Belgium tel. + 32
> 54/436 185 Thierry.Onkelinx at inbo.be www.inbo.be
>
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> be no more than asking him to perform a post-mortem
> examination: he may be able to say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
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> ~ Roger Brinner
>
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> extracted from a given body of data.
> ~ John Tukey
>
> -----Oorspronkelijk bericht-----
> Van: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org] Namens João Fadista
> Verzonden: dinsdag 8 april 2008 15:18
> Aan: r-help at r-project.org
> Onderwerp: [R] permutation test assumption?
>
> Dear all,
>
> Can I do a permutation test if the number of individuals in
> one group is much bigger than in the other group? I searched
> the literature but I didin´t find any assumption that refers
> to this subject for permutation tests.
>
>
> Best regards
>
> Ph.d. student
>
>
>
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